February 11, 2003
Saving for Retirement
We analyzed three basic plans:
Intertemporal Substitution
We modified the two goods - two prices diagram to study consumption in the present and consumption in the future. We assumed that all income was in the present. At 9:30, we found the amount of savings by maximizing utility and then watched as interest rates went down:
The lower interest rates did not last long. At 12:30, interest rates went up:
An increase in interest rates for a saver and a borrower with equal incomes in the two periods:
You can also put both agents on the same diagram:
Production Possibility Frontier
The Intertemporal Substitution diagram features a linear process for converting current wealth into future wealth. The tradeoff between current and future production might well be nonlinear for an individual engaged in actual physical (or mental!) activity. We capture this notion in the form of a Production Possibility Frontier. The idea is that giving up on some current production increases future production, but the effect diminishes as you give up on more and more current production.
Without access to financial markets, you would produce and consume at point A. With access to financial markets, you produce at P and consumer at C. Agents are happier if they have access to financial markets, and they might well work more when they are young.
A short explanation of why we picked the budget constraint that is tangent to the PPF:
Of these three budget constraints, the one through P gets the agent to the highest indifference curve.